名校
1 . 为提升城市景观面貌,改善市民生活环境,某市计划对一公园的一块四边形区域
进行改造.如图,
(百米),
(百米),
,
,
,
,
,
分别为边
,
,
的中点,
所在区域为运动健身区域,其余改造为绿化区域,并规划4条观景栈道
,
,
,
以及两条主干道
,
.(单位:百米)
,求主干道
的长;
(2)当
变化时,
①证明运动健身区域
的面积为定值,并求出该值;
②求4条观景栈道总长度的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d2c15801fee2405573677484f5dcfa4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef0402dd5ae3db10281f9f1e11738bcb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd95dc30c0344788b94289c464a3158e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cdb2dd10731b99c0f4f89ee957f8a239.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a2ec894b5364994873467dc3218a5ed6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1f2281cb6df0c3c518ce5ed19a02b57e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15a424b50eaeafa6f302ffd95476cb86.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b3533837e3d08c461dea031a44e5424d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b46c607b3deac746c0ef3389ad8f65c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c4c865445dda4a59b6d5cb18fd74404.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/72c4340dcffb0783d118a587e5352a2d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d39b8d91afc34e4a9b0fdbb6bafb9087.png)
①证明运动健身区域
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1f2281cb6df0c3c518ce5ed19a02b57e.png)
②求4条观景栈道总长度的取值范围.
您最近一年使用:0次
名校
解题方法
2 . 已知在非零数列
中,
,数列
的前
项和
.
(1)证明:数列
为等差数列.
(2)求数列
的通项公式.
(3)若数列
满足
,求数列
的前
项和
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/801fa9a32d801a4a6f1d8ddff5fcee40.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a25ff86d030aefcd645d64e8ccfeae3.png)
(1)证明:数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/41cf1da18d91f7c98086553d157d1a87.png)
(2)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
(3)若数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57ef6d44448092ebdb9e4a49d866a749.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4503d0f83aefff6d288c347781102025.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57ef6d44448092ebdb9e4a49d866a749.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
您最近一年使用:0次
名校
解题方法
3 . 函数
对任意实数
恒有
,且当
时,
.
(1)判断
的奇偶性;
(2)求证:
是
上的减函数;
(3)若
,解关于
的不等式
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b0fffbec1fe851795dfdd448bf0d165.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5be8e8e51ff9cf43529a75ce031f8865.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08115d6d9f876dea921a4d32260ff1fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a71baf6217604517fd98fa97d0f55b43.png)
(1)判断
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf3ed15aa3dcc4211fb520b5b942c989.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10bbdef421c976962a270a2beabbad91.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/130ea481fadd167c198f6855bba2f654.png)
您最近一年使用:0次
2023-11-03更新
|
1515次组卷
|
3卷引用:湖北省荆州市沙市中学2023-2024学年高一上学期11月期中数学试题
湖北省荆州市沙市中学2023-2024学年高一上学期11月期中数学试题广东省深圳市深圳大学附属实验中学2023-2024学年高一上学期期中数学试题(已下线)5.4 函数的奇偶性-【题型分类归纳】(苏教版2019必修第一册)
名校
解题方法
4 . 已知数列
的首项
,满足![](https://staticzujuan.xkw.com/quesimg/Upload/formula/faceffdd5b87d0520868b407acf87a3a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c90282d4a37c9a20620d4bbb0c263cae.png)
(1)求证:数列
为等比数列;
(2)记数列
的前n项的和为
,求满足条件
的最大正整数n.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5d0ae8af1b4dfc31c317fcbe291d28b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/faceffdd5b87d0520868b407acf87a3a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c90282d4a37c9a20620d4bbb0c263cae.png)
(1)求证:数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/213e22890204937a5dded4436369390f.png)
(2)记数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/41cf1da18d91f7c98086553d157d1a87.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/170f712746e4ffa8aa30c987a6474abd.png)
您最近一年使用:0次
解题方法
5 . 19世纪戴德金利用他提出的分割理论,从对有理数集的分割精确地给出了实数的定义,并且该定义作为现代数学实数理论的基础之一可以推出实数理论中的六大基本定理,那么在证明有理数的不完备性时,经常会用到以下两个式子,已知正有理数
,满足
,
,则下列说法正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1010846eeec6c9da29640f5aa3f8738.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2365d0c0f3df6550a7c8eb9eccaaa50.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/367f40d955f158ea6de89e9f69f0f894.png)
A.![]() | B.![]() |
C.![]() | D.![]() |
您最近一年使用:0次
解题方法
6 . 已知数列
满足
,
,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a4188680e5320653753ad0340439cb77.png)
(1)证明:
是等差数列;
(2)设
,求
前10项的和.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76aef4cdcb5af742ce28003b7b6c8c20.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a8a0eecb5b800fce9ae10aed86ffee62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/34b55b95d5bfdd7c129be36c54d4e519.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a4188680e5320653753ad0340439cb77.png)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f329b217e1051b23f0d61023cdc6e69.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10ba6e70c28fbde93e95e928e5c93374.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5ab0309e2cd35585ea9fb2cc3017abf.png)
您最近一年使用:0次
7 . 已知数列
满足:
,
.
(1)证明:数列
是等差数列;
(2)记
,
,求数列
的前n项和
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/039e4fe671d61e59b96ee525c9df43e8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/588e4f939835eeb5feefdb5d37c921e6.png)
(1)证明:数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/41cf1da18d91f7c98086553d157d1a87.png)
(2)记
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57908072f697998145c4605d891583fc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a37a59558292ad6b3d0978bfd7484990.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
您最近一年使用:0次
2023-12-22更新
|
1256次组卷
|
4卷引用:湖北省武汉市第六中学2023-2024学年高二上学期第4次月考暨期末联考模拟数学试题
解题方法
8 . 已知正项数列
的前
项和为
,且
.
(1)证明:数列
是等差数列;
(2)若数列
满足
,且
,求数列
的前
项和
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad3e8f5fcdb91435999452179f0c767e.png)
(1)证明:数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fd8dfb2af5bfd44046042a50e6edc1c4.png)
(2)若数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/77f0c361a81fca5f19b30436036d4356.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/59dd6c97d2ee3e74ba5730f1cbcc1d43.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7b9a6ab87e485254777f03150c095017.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
您最近一年使用:0次
9 . 若数列
满足:存在等比数列
,使得集合
元素个数不大于![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
,则称数列
具有
性质.如数列
,存在等比数列
,使得集合
,则数列
具有
性质.若数列
满足
,
,记数列
的前
项和为
.证明:
(1)数列
为等比数列;
(2)数列
具有
性质.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c1fd18a909cecbaee7115d6b15631d83.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5ab0309e2cd35585ea9fb2cc3017abf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a75786d2d4c9abbb9ddea89c3dd1e39.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2eb60c1a8dba48239b667dcf1235dd2d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c1fd18a909cecbaee7115d6b15631d83.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d46bf6ded2f869744c6c50785f974aa6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/41ad4f005f5def1e6c0d54610692c03d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/05d8a4d9c52ac3520d5b64c62499ecf0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b0b64100360c766baccac7c39255d8ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c1fd18a909cecbaee7115d6b15631d83.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3bea0dd7e474bcd04db2544427ba0488.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76aef4cdcb5af742ce28003b7b6c8c20.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d1bae03ee4ac75dacfb026290e4207dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1aa128888d2031f4c634be7f954238ad.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76aef4cdcb5af742ce28003b7b6c8c20.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
(1)数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2b24baee90fd506c597bd9bd7293e90a.png)
(2)数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d013861990cf331c82eb453416ae31bc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3bea0dd7e474bcd04db2544427ba0488.png)
您最近一年使用:0次
2024-01-13更新
|
832次组卷
|
4卷引用:湖北省武汉市江岸区2024届高三上学期1月调考数学试题
湖北省武汉市江岸区2024届高三上学期1月调考数学试题(已下线)压轴题数列新定义题(九省联考第19题模式)练河南省郑州市宇华实验学校2024届高三下学期第二次模拟考试数学试题(已下线)模型1 用综合法快解新情境背景下的数列创新题模型(高中数学模型大归纳)
名校
解题方法
10 . 已知数列
满足
.
(1)求
的通项公式;
(2)设
,记
的前
项和为
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf13f9de11d88dd4bd892162159f3908.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b4e5bb55dc85150de816e2d475e94aa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9ad3c385e1b05414bf7afd464126fd7e.png)
您最近一年使用:0次
2023-11-24更新
|
1438次组卷
|
6卷引用:湖北省宜昌市协作体2023-2024学年高三上学期期中考试数学试题